12th Maths Formulas List PDF

PDF Name	12th Maths Formulas List
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12th Maths Formulas List - Summary

12th formulas serve as powerful tools to solve complex problems and gain insights into various mathematical concepts. By mastering these 12th-grade math formulas, students can enhance their problem-solving skills.

Algebraic formulas, such as the quadratic formula, help find solutions to quadratic equations. Arithmetic and geometric progression formulas enable the computation of sums and terms in these sequences. Trigonometric identities, like the Pythagorean identities, establish relationships between trigonometric functions. Calculus formulas, including derivative and integration rules, are indispensable for analyzing rates of change and calculating areas. Probability and statistics formulas facilitate the interpretation of data and aid in making informed decisions.

Class 12th Maths Formulas Download

Here we have given the list of some formulas for 12th class Math.

Areas

Square			: length of side
Rectangle			: width : height
Triangle			: base : height
Rhombus			: large diagonal : small diagonal
Trapezoid			: large side : small side : height
Regular polygon			: perimeter : apothem
Circle			: radius : perimeter
Cone (lateral surface)			: radius : slant height
Sphere (surface area)			: radius

Volumes

Cube	$V = s^{3}$	$s$ : side
Parallelepiped	$V = l \times w \times h$	$l$ : length $w$ : width $h$ : height
Regular prism	$V = b \times h$	$b$ : base $h$ : height
Cylinder	$V = π r^{2} \times h$	$r$ : radius $h$ : height
Cone (or pyramid)	$V = \frac{1}{3} b \times h$	$b$ : base $h$ : height
Sphere	$V = \frac{4}{3} π r^{3}$	$r$ : radius

Functions and Equations for 12th Maths

Directly Proportional	$y = k x$ $k = \frac{y}{x}$	$k$ : Constant of Proportionality
Inversely Proportional	$y = \frac{k}{x}$ $k = y x$	$k$ : Constant of Proportionality
$a x^{2} + b x + c = 0$	Quadratic formula	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
	Concavity	Concave up: $a > 0$
	Concavity	Concave down: $a < 0$
	Discriminant	$Δ = b^{2} - 4 a c$
	Vertex of the parabola	$V (\frac{- b}{2 a}, \frac{- Δ}{4 a})$
$y = a {(x - h)}^{2} + k$	Concavity	Concave up: $a > 0$
	Concavity	Concave down: $a < 0$
	Vertex of the parabola	$V (h, k)$
Zero-product property	$A \times B = 0 \Leftrightarrow A = 0 \lor B = 0$	ex : $(x + 2) \times (x - 1) = 0 \Leftrightarrow$ $x + 2 = 0 \lor x - 1 = 0 \Leftrightarrow x = - 2 \lor x = 1$
Difference of two squares	$(a - b) (a + b) = a^{2} - b^{2}$	ex : $(x - 2) (x + 2) = x^{2} - 2^{2} = x^{2} - 4$
Perfect square trinomial	${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$	ex : ${(2 x + 3)}^{2} = {(2 x)}^{2} + 2 \cdot 2 x \cdot 3 + 3^{2} =$ $4 x^{2} + 12 x + 9$
Binomial theorem	${(x + y)}^{n} = \sum_{k = 0}^{n}^{n} C_{k} x^{n - k} y^{k}$

Probability and Sets for 12th Maths Formulas

Commutative	$A \cup B = B \cup A$	$A \cap B = B \cap A$
Associative	$A \cup (B \cup C) = A \cup (B \cup C)$	$A \cap (B \cap C) = A \cap (B \cap C)$
Neutral element	$A \cup \emptyset = A$	$A \cap E = A$
Absorbing element	$A \cup E = E$	$A \cap \emptyset = \emptyset$
Distributive	$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$	$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
De Morgan’s laws	$\bar{A \cap B} = \bar{A} \cup \bar{B}$	$\bar{A \cup B} = \bar{A} \cap \bar{B}$
Laplace laws	$P (A) = \frac{Number of ways it can happen}{Total number of outcomes}$
Complement of an Event	$P (\bar{A}) = 1 - P (A)$
Union of Events	$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
Conditional Probability	$P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$
Independent Events	$P (A ∣ B) = P (A)$	$P (A \cap B) = P (A) \times P (B)$
Permutation	$P_{n} = n! = n \times (n - 1) \times ... \times 2 \times 1$	ex : $P_{4} = 4! = 4 \times 3 \times 2 \times 1 = 24$
Permutations without repetition	$^{n} A_{p} = \frac{n!}{(n - p)!}$	ex : $^{6} A_{2} = \frac{6!}{(6 - 2)!} = 30$
Permutations with repetition	$^{n} A_{p}^{'} = n^{p}$	ex : $^{5} A_{3}^{'} = 5^{3} = 125$
Combination	$^{n} C_{p} = \frac{^{n} A_{p}}{p!} = \frac{n!}{(n - p)! \times p!}$	ex : $^{5} C_{4} = \frac{^{5} A_{4}}{4!} = 5$
Probability Distribution	Average value	$μ = x_{1} p_{1} + x_{2} p_{2} + ... + x_{k} p_{k}$
Probability Distribution	Standard deviation	$σ = \sqrt{\sum_{i = 1}^{k} p_{i} {(x_{i} - μ)}^{2}}$
Binomial distribution	$P (X = k) =^{n} C_{k} . p^{k} . {(1 - p)}^{n - k}$	ex : $B (10; 0, 6)$ $P (X = 3) =^{10} C_{3} \times 0, 6^{3} \times 0, 4^{7}$